Abstract: The conduction electrons in Si are not in a well-defined single Bloch state. Instead, the Si conduction band is six-fold degenerate, with minima (valleys) along the x, y and z crystallographic directions. This imposes limitations to the spin manipulation and coherence. It was recently proposed to encode quantum information directly into the valley degree of freedom, converting the spurious valley Hilbert subspace into a useful ingredient for a quantum computer. In this talk, valley degrees of freedom in Si are addressed in 3 different contexts.

1) Based on an atomistic pseudopotential theory, we demonstrate that ordered Ge-Si layered barriers confining a Si slab can be optimized to enhance the VS in the active Si region by up to one order of magnitude compared to the random alloy barriers adopted so far. We identify Ge/Si layer sequences leading to a VS as large as ~9 meV. The splitting is "protected" even if some mixing occurs at the interfaces.

2) Interface states form spontaneously at some semiconductor-barrier interfaces and they may improve or hinder the electron control and coherence for semiconductor-based qubits. From a simple 1D Tight-binding model, new insights emerge regarding the interface state's energy, as well as the exponential longer (shorter) localization lengths into the Si (barrier) material. The interface state may be probed experimentally by an external electric field, which modulates the capacitance of the system and the lowest level spacing (valley splitting).

3) We analyze the valley composition of one electron bound to a shallow donor close to a Si/barrier interface. A full six-valley effective mass model Hamiltonian is adopted. For low fields, the electron ground state is essentially confined at the donor. At high fields the ground state is such that the electron is drawn to the interface, leaving the donor practically ionized. Valley splitting at the interface occurs due to the valley-orbit coupling, taken here as a complex parameter. A sequence of two anti-crossings takes place and the complex phase affects the symmetries of the eigenstates and level anti-crossing gaps.